ABSTRACT
SUN, XIAO‐YU. Concurrent and Sequential Surface Modification of Electrospun Polymer Micro/Nano‐Fibers. (Under the direction of Prof. Richard J. Spontak.)
Surface modification of nano‐fibers with bioactive functional groups has become an
arresting research area in recent decades, which provides possibility for the invention of
bioactive materials for textiles and biomedical applications e.g. tissue engineering. The
major objective of this research is to develop a novel single‐step processing route for the
production of synthetic fibers possessing specific bioactive surface functionalities at
nano/submicron scale. Unlike traditional sequential surface modification of nanofibers,
sequence‐defined oligo‐peptide that carries biofunctionality was synthesized separately
before incorporated onto the electrospun fibers as surface functionalities by a single‐step
spinning process, so as to avoid the effect from chemical synthesis on fiber processing. As
one of the most widely‐used technologies for the production of polymeric nanofibers,
electrospinning was chosen to achieve the single‐step surface modification. Conventional
homopolymer in conjunction with the biofunctional oligopeptide‐incorporated block
copolymer were co‐electrospun. Nanofibers at submicron scale with surface enrichment of
block copolymer were achieved due to phase separation caused by polarizability difference
under static electric field. The surface segregation of peptide block was proved by the
nitrogen enrichment measured from X‐ray Photoelectric Spectroscopy (XPS). The proposed
mechanism is discussed based on mainly the model homopolymer system of polyethylene
oxide (PEO), and extended to the ternary polymer blends composed of thermoplastic
polymethyl methacrylate (PMMA), PEO and block copolymer. The surface modification
technique introduced deep insight into the electrospinning process with its effect to the
polymer blends microphase separation, and leads to a promising perspective for
biomaterial engineers to produce nanofibers with certain surface bio‐functional groups.
Copy Right Reserved©
Concurrent and Sequential Surface Modification of
Electrospun Polymer Micro/Nano‐Fibers
by
Xiao‐Yu Sun
A dissertation submitted to the Graduate Faculty of North Carolina State University
In partial fulfillment of the Requirements for the degree of
Doctor of Philosophy
Chemical Engineering
Raleigh, North Carolina
February, 2008
APPROVED BY:
________________________________ ______________________________ Dr. Richard J. Spontak Dr. Saad A. Khan
Committee Chair
DEDICATION
To my father, Jiadong Sun
致父亲孙甲东
BIOGRAPHY
Xiao‐Yu Sun was born to Jiadong Sun and Jingzhou Ye, both high school teachers in
mathematics and biology respectively, in Haerbin, which is known as “ice city” in the
northeast part of China in 1977. Then the family moved to Hangzhou, a beautiful city full of
green in southeast China. After high school she was accepted to Tsinghua University in
Beijing and obtained both Bachelor of Science and Master of Science degree major in
Chemical Engineering. She achieved the best senior design award and many scholarships
during the years in college. In 2002 she joined TH‐UNIS Insight Co. Ltd. and worked for two
years as a chemical engineer. She contributed her knowledge to help with the design and
scale‐up of two product lines of chemical intermediates.
In January 2004 Xiao‐Yu Sun came to US and became a graduate student in the PhD
program of Chemical and Biomolecular Engineering Department at North Carolina State
University. She has been working on the electrospinning of polymer blends with specific
surface modification of biofunctionalities since she joined the polymer morphology group to
work with Dr. Richard J. Spontak. By her 4th year she had one book chapter on surface characterization technology, one book chapter on nanofiber technology, and 2 papers
published on high profile journals with another 2 submitted. She is going to start her career
in SABIC Innovative Plastics (formerly GE Plastics) as a product developer in the company’s
research and development site in Mr. Vernon, IN.
ACKNOWLEDGMENTS
My deepest thankfulness hereby goes to my advisor Dr. Richard J. Spontak. Without
his guidance into the macromolecule world, none of those following chapters would be
presented as they are. During the four years at NC State, I gradually learned from him the
polymeric materials and alloys, and how to applied the knowledge into my own research.
He has also been the major advisor for me, an international student, on all sorts of
American regulations from a proper noun to certain custom of this society. From him I
understood professionalism as well as the appropriate way of dealing with various types of
circumstances or resources especially when they happen all together, and that perfection is
never perfect.
My second deepest thankfulness goes to other professors and graduate students
who have offered absolutely necessary and selfless help to my research. Without their
assistance there would have been no possibility to finish my study. I’d like to express my
appreciation to: Dr. Tushar Ghosh and Ravi Shankar for initiating the electrospinning setup;
Dr. Hans Börner for the synthesis of the biofunctional peptide conjugate; Dr. Gregory
Parsons and Qing Peng for the creative idea of ALD sequential surface modification on my
electrospun fibers; Dr. Orlin Velev for his guidance on electrokinetics and Suk Tai Chang for
his cooperative work on the electric field simulation by FEMLAB; Dr. Saad Khan, Sachin
Talwar and other group members for the assistance with rheology measurements and
electrospinning fellowship; Dr. Jan Genzer and his GIRLS for the spin coater and other
abundant instruments. My special thanks to our own group members of the Fellowship of
Polymer Morphology: Anand Patel, Arjun Krishnan, Bin Wei, Evren Özçam, Juan Waver,
Kristen Roskov, Michelle Bowman, Omer Gozen and Renee Nobles, who also provided
numerous help and laughter that makes our office the most enjoyable place to be.
I am also quite grateful to have spent my PhD years in this friendly department filled
with not only knowledgeable and respectable professors, but also lovely and careful staffs.
Ms. Sandra Bailey, Diane Harper, Shirley Kow and Saundra Doby are the sweetest ladies I
have ever met in this country. Mr. Kit Yeung told me a lot of interesting stories while I was
an anxious new bee. My fellow Chinese friends offered their helping hand and soothed me
with their love and care that made me feel I am not alone. Bin Wei introduced me to his
advisor who became my advisor; Haiou Yang & Zushou Hu helped me from finding the first
apartment; and Qing Peng, Fei Shen & Puxuan Dong surprised me with a birthday party. In
my personal life, I spent most of the weekends with volleyball teammates, tennis partners
and friends. Amy Yuen, Xiao Fu, Yu Liu, Zhen Cheng, Rongrong Zhou, Yuee Feng, Chen Ruan,
Yingjie Li, Lei Ji…There are just too many names I would like to mention here to express my
heartful appreciation for the time you spent with me and the joy you brought that will
always keep shimmery in my memory.
Last but not the least; I would like to acknowledge my family members for their
ultimate support. There is no way to fully express my feelings to my dearest family for their
mental supports as always, and especially physically being here during the last few months
of my PhD. It was a little bit crowded but also filled my heart with warmth, tranquility, faith
and energy. It was the long term support from my parents, SUN Jiadong and YE Jingzhou,
that encouraged me to independently go through all the tortuosities in my life; it was the
faith, understanding and patience from my husband ZHENG Yu that accompanied me
through all these years.
TABLE OF CONTENTS
LIST OF TABLES………....……….………...………ix
LIST OF FIGURES……….……….………...x
CHAPTER I: Structure, Processing, & Properties of Polymer Nanofibers for Emerging Technologies……….……….……1
1. Introduction to Nanofibers……….…………...1
2. Processing ……….……….………....3
2.1. Overview of Nanofiber Processing……….….3
2.2. Electrospinning Technology……….………5
2.2.1. History of Electrospinning……….……….………5
2.2.2. Fundamentals of Electrospinning……….……….………..8
2.2.3. Modeling of Electric‐Driven Jet……….……….………10
2.2.4. Fiber Morphology Control……….……….………13
2.2.5. Electrospinning Setup Design……….……….………18
2.2.6. Material Systems……….……….……….…………..20
3. Properties……….……….……….……….…………31
3.1. Mechanical Properties……….……….……….………..31
3.2. Thermal Properties……….……….……….……….33
3.3. Other Properties……….……….……….……….34
3.4. Characterization of Nanofibers……….……….……….34
4. Applications……….……….……….……….…….36
4.1. Scaffolds in tissue engineering……….……….……….36
4.2. Controlled encapsulation and delivery of biological agents……….……….38
4.3. Bioactive textiles……….……….……….………..40
4.4. Biosensor……….……….……….………..41
4.5. Filtration……….……….……….………...42
Nomenclature……….……….……….……….44
Tables……….……….……….………..47
Figures……….……….……….……….57
References……….……….……….………74
CHAPTER II: Electrospinning of Biomaterial Nanocomposite Fibers: Morphology, Structure and Surface Modification……….82
1. Introduction………82
2. Electrospinning Fundamentals………84
2.1. Theory………..…84
2.2. General Morphological Control………..………86
2.2.1. Manipulation by material properties………..87
2.2.2. Manipulation by operational parameters………88
3. Multi‐Component Electrospinning……….90
3.1. Electrospinning of Synthetic Polymers……….….90
3.1.1. Homopolymers……….90
3.1.2. Copolymers………91
3.1.3. Polymer Blends………94
3.1.4. Polymer with Nanocomposite Fillers……….96
3.2. Electrospinning of Natural Polymers………..98
3.3. Biomaterial‐Composite Nanofibers….………99
4. Surface Modification of Electrospun Nanofibers……….…….101
4.1. Design Criteria of Surface Modification for Bio‐interfaces………..101
4.2. Surface Modification via Electrospinning……….…………103
4.2.1. Core‐sheath structures by coaxial electrospinning……….103
4.2.2. “Self‐organized” surface modifications………106
4.3. Post‐spun Surface Modification……….……….108
Figures……….…….……….………..111
References………119
CHAPTER III: Field‐Driven Biofunctionalization of PEO Fiber Surfaces during Electrospinning ………125
References………137
CHAPTER IV: Attachment of Biofunctionalities onto Thermoplastic PMMA/PEO Nanofibers: F i e l d‐D r i v e n S u r f a c e M o d i f i c a t i o n i n t h e E l e c t r o s p i n n i n g o f PEO/PMMA/FC3EO Ternary Polymer Blends ………141
References………156
CHAPTER V: In‐Situ Surface Modification of Microfibers Electrospun from Ternary Polymer Blends Containing a Peptide‐Polymer Conjugate ………...158
References………185
CHAPTER VI: A Systematic Study of Electrospinning of Polyethylene Oxide (PEO) with different Pure and Binary Solvent Mixtures ………187
References………211
CHAPTER VII: Mechanism of Surface Segregation during Electrospinning: Electrophoresis and Dielectrophoresis of Biopolymer Molecules with Different Polarizability ………..………..213
References……….244
CHAPTER VIII: Conclusions & Future Work……….245
APPENDIX I: Atomic Layer Deposition on Electrospun Polymer Fibers as a Direct Route to Al2O3 Microtubes with Precise Wall Thickness Control ……….254 References………266
APPENDIX II: Preliminary Investigation on the Synthesis of Biodegradable Polylactide‐ peptide Block Copolymers by a Novel Method………268
BIBLIOGRAPHY………276
LIST OF TABLES
Chapter I
Table 1. Effects of material properties on electrospun fiber morphology……….47
Table 2. Effects of operational parameters on electrospun fiber morphology………..49
Table 3. Electrospinning of homopolymers……….51
Table 4. Electrospinning of copolymers……….53
Table 5. Electrospinning of polymer blends………...54
Table 6. Common techniques for nanofiber characterizations………...55
Chapter VI Table 1. Pure solvent data ……….……….196
Table 2. Binary solvent data ……….196
Table 3. Solubility parameters of binary solvent systems at different temperature …...196
Table 4. Average diameter and morphology of electrospun fibers at ET ………...…………..197
Table 5. Average diameter and morphology of electrospun fibers at RT ……….…...197
Chapter VI Table 1. Material properties of homopolymers and solvents ………226
LIST OF FIGURES
Chapter I
Figure. 1 Increase of electrospinning research literature. Data obtained from ISI Web of Science directory and SciFinder Scholar respectively. ………57
Figure. 2 Nanofibers produced by different methods. A) Schematic illustration of Self‐ assembling peptide surfactant/detergents that form well‐ordered structures including nanotubes with openings, nanovesicles and micelles300. B) SEM micrograph of PLLA fibrous matrix prepared from phase separation of 2.5% w/v PLLA/THF solution16. ……….58
Figure. 3 a) Schematic figure of basic electrospinning setup. b) Photograph of a typical plate‐to‐plate electrospinning setup……….59
Figure. 4 High‐speed and low‐speed photographs of electrospinning instability region. a. low speed photograph with exposure time=1/250s; b. high speed photograph with exposure time=18ns c. overlapping the high and low speed photograph of the instability region. Dark thread taken at 18ns and white splaying background taken at 1/250s.41. ………60
Figure. 5 Simulated jet path comparison. a) Simulation accounting for solvent evaporation and polymer solidification; b) Simulation without accounting for solvent evaporation and polymer solidification.60……….……….61
Figure. 6 SEM micrographs showing the elimination of beads structure in the PVP electrospun fibers with the increase of concentration in 16/3 ethanol/water (by volume) solution. A) 3wt%; B) 5wt%; C) 7wt%; and D) 5wt% with 0.35 mg/ml of tetramethylammonium chloride48. ……….………...62
Figure. 7 Correlation between the rheology of linear or branched polyester solution and electrospun fiber morphology control. a) Dependence of specific viscosity on concentration fro branched PET‐co‐PEI (Mw=46,000 g/mol and g’=0.8), with changes in the slope marking the onset of the semidilute unentangled, semidilute entangled and concentrated regimes of the solution. b) Dependence of fiber diameter on the normalized concentration for the PET‐co‐PEI series that satisfies a 2.6 power law relationship72. ……….………63
Figure. 8 Photos for multiple jet electrospinning. a) Photograph of a nine‐jet electrospinning matrix showing the interaction between the electrospinning jets92; b) Photograph of a ceramic “cylindrical porous tube” setup90. ……….64
Figure. 9 Core‐shell structured nanotubes created by coaxial electrospinning. A) Schematic illustration of the setup; B) TEM image of two as‐spun hollow tubes made of TiO2/PVP composites, after the oily cores had been extreacted with octane. C) TEM image of TiO2 tubes after PVP removed by calcining at 500 oC D) SEM image of anatase tubes 47. ……….65
Figure. 10 Schematic electrospinning setup (i). corresponding electric field and (ii) photographs of electrospun fibers (iii): a) Classic point‐to‐plate setup109; b) Multiple‐ electrodes setup109; c) Silica grid setup45; d) Rotating disk collector setup 116. ………66
Figure. 11 Collector designs and corresponding micrographs of the aligned fibers. a).Wire drum collector with copper wires collecting electrospun nylon nanofibers; SEM of axially aligned fibers showing at right 115. b).Cross pattern of collector electrodes with SEM of uniaxially aligned and cross‐woven fibers showing at right 119; c).Dual ring collector and formed yarns 123. d) Rotating disk collector for DNA molecules aligned and embedded in PEO electrospun fibers with fluorescence micrographs132. ………...68
Figure. 12 Electrospinning of copolymer and polymer blends. A) SBS triblock copolymer displaying axis‐oriented PS phase domains after annealing for 1hr at 70oC150. B) TEM images of cross section of fibers spun from 30 wt% THF solution of PS‐b‐PI with 29% PI content, showing the microphase separation151. C) Superhydrophobic surface created by coelectrospinning of PS/PMMA‐b‐PS polymer blends. Upper and bottom image shows water droplet sliding on 17o‐tilted surface of PS/PMMA‐b‐PS and pure PS electrospun fiber mat respectively at same unmarked size scales153; D) Comparison of (a) as‐spun and (b) water‐ treated 50/50 PAN/PEO bicomponent fibers from 8% DMF solution. Water‐extracted PEO left elongated pores on the surface and inside the fiber 299. ..……….………..69
Figure. 13 Electrospinning of inorganic nanocomposite fibers. a) SEM image of V2O5‐ TiO2‐Ta2O5 nanocomposite fibers by Xia’s group173. b) TEM image showing Growth of CNT on CNF produced by the electrospinning, carbonization of PAN fibers followed by catalytic growth of CNT186. c) TEM image showing the aligned SWCNT in PAN nanocomposite fiber187. d) TEM image showing the well‐alignment of 10% MWCNT in PAN electrospun nanocomposite fibers185. e) Macroscale photograph of electrospun copper fibers at submicron scale177. f) Macroscale photograph of electrospun PAN/MWCNT nanocomposite fiber sheets containing MWCNT: 1, 0%; 2, 2%; 3, 3%; 4, 5%; 5, 10%; 6, 20%185. ...….70
Figure. 14 Surface modification of electrospun nanofibers. Electrospun fiber mat of Bombyx mori silk and PEO blends before (A) and after (B) surface methanol treatment.500× magnification. 5μm scale bar43……….………...71
Figure. 15 Specific designs of nanofiber characterizations. a) A series of images taken for a tensile test of an individual electrospun PA66 (nylon‐6,6) nanofiber up to the break point222. ………..………72
Figure. 16 Application of polymer nanofibers. A) LSCM micrographs showing the alignment of immunostained α‐actin filaments in SMCs after 1 day of culture on the aligned electrospun nanofibers51. B) Fluorescent micrograph showing the enraptured E. coli cells inside PVA electrospun nanofibers which remained bioactivity after electrospinning266. C) Morphology of HEPM cells on gelatin nanofiber matrices, showing the cells attaching, spreading and forming oriented monolayers with typical fibroblastoid morphology257. D) Encapsulation of hydrophobic liquids in hydrophilic polymer nanofibers by coaxial electrospinning262………73
Chapter II
Figure. 1 Schematic graph of basic electrospinning process….………111
Figure. 2 Different morphologies of electrospun fibers. A) Helical structured electrospun fibers composed of 8.5 wt % PEO and 0.75 wt % poly (aniline sulfonic acid) from aqueous solution64. B) Ribbon‐shaped electrospun fibers from 10 wt% poly (ether imide) in hexafluoro‐2‐propanol solutions66. C) Beads‐on‐the‐string morphology of electrospun PEO fibers from aqueous solutions with viscosity of 74 centipoises37. D) Porous surface structures of PS electrospun fibers controlled by humidity during electrospinning67. ………..……….112
Figure. 3 Electrospinning of copolymers. A) SBS triblock copolymer displaying axis‐ oriented PS phase domains after annealing for 1hr at 70oC118. B) TEM images of cross section of fibers spun from 30 wt% THF solution of PS‐b‐PI with 29% PI content, showing the microphase separation123. C) SIS triblock copolymer showing concentric (upper fibers) and spherical microphase separation behavior both at cross section and along axis124. Size of the scale bar: 100nm. ………...……….113
Figure. 4 Electrospinning of polymer blends and nanocomposites. A) Residual PLA fiber after selective removal of PVP (original ratio PVP/PLA=5:1) showing co‐continuous structure within the fiber blends29. B) Comparison of (a) as‐spun and (b) water‐treated 50/50 PAN/PEO bicomponent fibers from 8% DMF solution. Water‐extracted PEO left elongated pores on the surface and inside the fiber, at the same time decreased the averaged fiber
diameter from 390 nm to 130 nm129. C) TEM image of core‐sheath structure with the OsO4‐ stained PANI appearing to be the dark core area and light PS as sheath131. D) Bright field TEM images showing the alignment of montmorillonite layers in the nylon 6‐ montmorillonite electrospun nanocomposite fiber 65. ………114
Figure. 5 SEM micrographs showing interactions between normal human oral keratinocytes (NHOK) and electrospun collagen fiber mat as ECM. Upper graphs are with collagen nanofibers only; Bottom graphs are with ECM protein‐coated (type I collagen or laminin) nanofibers, from which better cell migration can be observed within 3 days and faster cell growth underneath the fiber mat can be observed within 7 days. ……….115
Figure. 6 Schematic presenting the heterobifuntional PEG‐PLA block copolymer for constructing functional PEG on the biomaterial surface 216. ………..……….116
Figure. 7 A typical coaxial electrospinning setup 220 and compounded pendant drop at the coaxial tip 225……….……….117
Figure. 8 A) TEM micrograph of hollow anatase nanotubes after coaxial electrospinning with mineral oil as the core material, followed by the calcination of PVP‐ titania composites224. B) Biomemetic multi‐channel fibers by coaxial electrospinning230. C) Superhydrophobic surface created by coelectrospinning of PS/PMMA‐b‐PS polymer blends. Upper and bottom image shows water droplet sliding on 17o‐tilted surface of PS/PMMA‐b‐ PS and pure PS electrospun fiber mat respectively at same unmarked size scales117. D) Confocal laser scanning microscopy (CLSM) image showing the core‐sheath structure created by emulsion electrospinning. Core contains FTIC labeled PEO with PEG‐b‐PLLA as the sheath233. E) Optical microscopy graph showing PMMA/PAN emulsion in DMF after mixing two homogeneous solutions of 6 wt% PMMA/DMF and PAN/DMF together after one day. PAN/DMF is the continuous phase in the emulsion235. F) TEM and SEM micrographs showing the “nanoporous‐structured” morphology formed by electrospinning of PMMA/PAN‐co‐PMMA blends in a nano‐co‐continuous way followed by carbonization 236. ……….………..……….118
Chapter III
Figure. 1 Schematic illustrations of single‐step surface modification during electro‐ spinning and the peptide‐functionalized PEO microfibers produced therefrom. In the experimental setup, electrospinning is conducted horizontally, not vertically. Peptide segments attached to the microfiber surface are expected to appear as short hairs, rather than the long hairs depicted here. ………134
Figure. 2 SEM images of electrospun PEO/(SEE)3‐PEO microfibers generated from two PEO solution concentrations (in g L‐1): 30 (top row) and 40 (bottom row). The concentrations of added (SEE)3‐PEO are (in wt% relative to the PEO): (A,E) 1, (B,F) 2, (C,G) 3 and (D,H) 5. An AFM height image obtained from a single microfiber is included in the inset in (C). The SEM image in the inset of (G) shows the effect of reversed field polarity at the same magnification. .……….…..………..…….135
Figure. 3 In (A), high‐resolution XPS nitrogen scans acquired from electrospun PEO/(SEE)3‐PEO microfibers produced from 30 g L‐1 PEO solutions with 1‐3 wt% (SEE)3‐PEO (each scan is labeled). The additional XPS trace (blue) corresponds to a solution (30 g L‐1 PEO solution with 2 wt% (SEE)3‐PEO) spun‐cast onto silicon wafer. Gaussian curve fits to the data are included (green). An XPS survey scan is displayed in (B) for microfibers generated from a 30 g L‐1 PEO solution with 5 wt% (SEE)3‐PEO. The inset is an enlargement of the nitrogen peak. In (C), the nitrogen surface concentration measured by XPS is presented as a function of (SEE)3‐PEO content at two PEO solution concentrations (in g L‐1): 30 ( ) and 40 ( ). The solid lines denote regressed fits to an exponential rise (through the origin), and the dashed line represents the nitrogen concentration in the bulk PEO microfibers calculated from the (SEE)3‐PEO concentration. The magenta area provides an estimate of the instrument detection limit. ………...……….136
Chapter IV
Figure. 1 Fluorescent image obtained by laser‐scanning confocal microscopy ( λ = 494 nm) of electrospun PEO/FC3PO fibers illustrating nitrogen, and hence peptide, enrichment on the surface of the fibers. ….………152
Figure. 2 SEM images of PMMA fibers electrospun from DMF solutions varying in PMMA concentration (in wt%): (A) 4, (B) 6 and (C) 8. The mean fiber diameters measured from images such as these are provided in the text. .……….…..………..…….153
Figure. 3 SEM images of 50/50 w/w PEO/PMMA fibers electrospun from 4 wt% solutions in DMF before (A) and after (B, C, D) water immersion at ambient temperature. Times for water immersion are 2 h (C) and 30 days (D). ………...……….154
Figure. 4 High‐resolution XPS nitrogen spectra (A, C) and SEM images (B, D) of PMMA/ PEO/FC3PO fibers electrospun at ambient temperature from solutions varying in polymer concentration and composition: (A, B) pure PMMA with 5 wt% FC3PO prepared from a 5 wt% solution in DMF; (C, D) 20/80 PMMA/PEO with 5 wt% FC3PO prepared from a 4 wt% solution in DMF. ……….………..155
Chapter V
Figure. 1 Viscosity reduction of solutions of PMMA/PEO blends in DMF with increasing PMMA concentration. In all cases, the total polymer concentration is maintained at 4 wt%. ………….….………165
Figure. 2 SEM micrographs of binary PMMA/PEO electrospun fibers. PMMA/PEO weight ratio is: a) 100/0; b) 90/10; c) 80/20; d) 60/40; e) 50/50; f) 30/70; g) 20/80; h) 0/100. .……….…..……….…..…….168
Figure. 3 Average fiber diameter and standard deviation of electrospun PMMA/PEO fibers change with PMMA content in the PMMA/PEO blends. ………...……….169
Figure. 4 Field‐emission SEM micrographs of 50/50 PMMA/PEO fibers after water immersion to remove the PEO. a) Same fibers with b) at lower magnification showing that the fiber structure can be retained after removal of PEO. ……….……….…..………170
Figure. 5 Optical microscopy images of spun‐cast films with different PMMA/PEO weight ratio at fixed FC3PO concentration of 5 wt%. in the ternary blends. DMF was used as solvent. PMMA/PEO weight ratio equal to: a) 100/0; b) 90/10; c) 80/20; d) 70/30; e) 60/40; f) 50/50; g) 40/60; h) 30/70; i) 20/80; j) 10/90; k) 0/100………...173
Figure. 6 a) Fiber diameter change with PMMA content in both binary and ternary electrospinning due to b) solution (in DMF) viscosity decrease with the increase of PMMA content in the blends. The binary PMMA/PEO (▲) and ternary PMMA/PEO/FC3PO (□) solutions show similar reduction of viscosity, while the viscosity of the ternary solutions decreased even more by the addition of FC3PO. ...………...……….176
Figure. 7 SEM micrographs of ternary PMMA/PEO/FC3PO electrospun fibers. PMMA/PEO weight ratio is: a) 100/0; b) 90/10; c) 80/20; d) 70/30; e) 50/50; f) 40/60; g) 20/80; h) 0/100. ……….………..………..……177
Figure. 8 Surface enrichment (△) of nitrogen content compared to bulk nitrogen (○) atom percentage in the blends, as well as diameter (◇) change of the ternary electrospun fibers with regard to the PMMA concentration increase in the PMMA/PEO/FC3PO blends. ………179
Figure. 9 High resolution regional scan of C1s peak of carbon element on the PMMA/FC3PO electrospun fiber surface. C1s peak can be divided to three peaks indicating
C‐C, C‐O, C=O respectively. Nitrogen scan is also shown to indicate if peptide conjugate can be detected on the fiber surface. The fibers were electrospun from solution with fixed 5 wt% of FC3PO in the polymer blends and PMMA/PEO weight ratio equal to: A. 100/0; B. 50/50; C. 30/70; D. 92/3, the optimal composition. ………181
Figure. 10 Surface PMMA weight ratio change in the electrospun ternary PMMA/PEO/FC3PO fibers. The red dot line indicates the bulk PMMA weight ratio vs. PEO. ………...………183
Chapter VI
Figure. 1 Illustration of conventional electrospinning setup. ….……….…198
Figure. 2 Conventional electrospinning setup schematic showing non‐uniform electric lines of force b) Illustration of the parallel plate setup. .………....………..…….199
Figure. 3 Illustration of the parallel plate setup. …….………...……….199
Figure. 4 Pictorial demonstration of electrospinning with different solvent systems. ……….200
Figure. 5 Variation of viscosity with PEO concentration and temperature. Solid and open symbol represent ET and RT data, respectively. Solid lines represent the exponential curve fit. a) Acetone‐HPLC binary solvent, b) Isopropanol‐HPLC binary solvent, c) Ethanol‐ HPLC binary solvent, d) Methanol‐HPLC binary solvent, e) HPLC grade water……….202
Figure. 6 Viscosity variation with solubility parameters for different solvent systems. All the filled and open symbol correspond to ET and RT polymer solution, respectively. Green and orange line represents the exponential fits for 1, 2, and 4% concentration viscosities. ……….………..………...203
Figure. 7 Variation of viscosity with applied electric field. Filled symbols indicates ET conditions, while open symbols shows RT. ………203
Figure. 8 Variation of Electric field with Q. Filled symbols indicates ET cases, while open symbols represent RT cases. ………..…204
Figure. 9 Viscosity variation with respect to Q. Filled symbols indicates ET cases, while open symbols represent RT cases. ………...205
Figure. 10 Electrospun PEO fibers with acetone‐Hplc binary solvent systems. Both top figs. are RT cases. Both bottom figs. are ET cases. Figs. a) and c) represent 1 wt % PEO concentration micrographs. Figs. c) and d) display 2 wt % PEO concentration micrographs. Scale markers are a) 500 nm, b) 1 μm, c) 1 μm, and d) 500 nm. ………...206
Figure. 11 Electrospun mats of PEO with isopropanol‐Hplc solvent system. Figs. (a‐c) RT cases and (d and e) ET cases. Figs. (a and d), (b and e), and c) represent 1, 2, and 4 wt % PEO concentration cases. Scale markers are (a‐c) 1 μm, d) 5 μm, and e) 500 nm. ………..207
Figure. 12 Micrographs of the electrospun PEO mats with ethanol‐Hplc solvent system. RT cases are presented in figs. (a and c), while ET cases in figs. (c and d). Figure a), (b and c), and d) displays 1, 2, and 4 wt % PEO concentration electrospun web, respectively. Scale markers are a) 5 μm, (b and d) 1 μm, and c) 500 nm. ………...208
Figure. 13 PEO Electrospun mats for methanol‐Hplc solvent system. Figs. (a and b) are RT cases, while figs. (c and d) are ET cases. Micrographs (a and c) and (b and d) represent electrospun mats having 1 and 2 wt % PEO, respectively. Scale markers are (a, b, and d) 1 μm and c) 500 nm. ……….209
Figure. 14 SEM micrographs of electrospinning of PEO wit Hplc grade water. Both the top micrographs represent RT case, while both the bottom micrographs display ET case. Figs (a and c) and (b and d) corresponds to PEO 1 and 2 wt % concentration electrospun mats. Scale markers are (a and c) 5 μm and (b and d) 2 μm. ……….210
Chapter VII
Figure. 1 Schematic drawing showing the induced dipole moment directions with regard to the polarizability of the particle and dielectrophoresis2. a) Parallel direction when particle has a higher permittivity than the medium; b) Reverse direction when particle has a lower permittivity than the medium. c) Positive dielectrophoresis; d) Negative dielectrophoresis. ….……….216
Figure. 2 Forces on the particles suspending in charged fluid medium. The collective forces of electrostatic, friction and Electrophoretic forces determines the movement of the c h a r g e d p a r t i c l e i n a n e l e c t r i c f i e l d . F i g u r e o r i g i n a l l y q u o t e d f r o m http://en.wikipedia.org/wiki/Image:Electrophoresis.gif. No copy right is required for reuse since the author has granted it to public. ………..……….…..………..…….218
Figure. 3 Molecular structures of the PEO‐oligopeptide block copolymers. a) C3PO; b) FC3PO. ………...……….228
Figure. 4 Electrospinning setup and the electric field. Parallel setup: a) Macroscale; b) Magnified region close to the spinneret tip; Point‐source to plate setup: c) Macroscale; d) Magnified region close to the spinneret tip. ……….………...233
Figure. 5 Comparison between parallel plates and point source setups: simulation of the electric field of electrospinning setups with polymer solution jet close to the Taylor cone region. a) Parallel plates setup; b) Point source setup; c) Cross sectional electric field change that’s showing a steep electric field change close to the interface between the polymer solution and surrounding environment of atmosphere (The white area on the left is having electric field lower than the lower limit color of dark blue). ……….236
Figure. 6 Comparison among different dielectric constants: simulation of the electric field of point source electrospinning setups with polymer solution jet close to the Taylor cone region. a) ε2=40; b) ε3=5; c) Comparison among different dielectric constants representing: ε1=80, aqueous solution; ε2=40, DMF solution and ε3=5, polymer melts (The white cavities are area with electric field intensity higher than the higher limit). ………237
Figure. 7 Comparison between Taylor cone and sharper cone shapes: simulation of the electric field of electrospinning setups with polymer solution jet close to the Taylor cone region. a) Taylor cone with 49.3o as half tangential angle; b) Sharper cone with 33.3o as the half tangential angle; c) Cross sectional electric field change that’s showing a steep electric field change close to the interface between the polymer solution and surrounding environment of atmosphere (The white area on the left is having electric field lower than the lower limit color of dark blue. ………...238
Figure. 8 Schematic of the C3PO ions in the aqueous polymer solution flow within the nozzle before and after Taylor cone. Dielectric constant of polymer solution was set to ε1=80. ………..241
Figure. 9 Fibers electrospun from polymer blends solutions that have been proved to be surface enriched with one of the component with high polarizability. A. PEO/FC3PO fibers with surface enrichment of FC3PO from 5 wt% bulk to 7.75 wt% on the surface; B. PMMA/FC3PO fibers with surface enrichment of FC3PO from 5 wt% in bulk to 9.9% on the surface; C. PEO/RGD3PO from 5 wt% in bulk to 15 wt% on the surface. ……….242
CHAPTER I
Structure, Processing, & Properties of Polymer Nanofibers for Emerging Technologies
1 INTRODUCTION TO NANOFIBERS
In the history of material science research, for application purposes research interests
of polymeric material physics have been focusing mainly on how to manipulate the material
properties at macro‐ or micro‐scale. Whereas in the recent decades, the “nano‐scale”
popped out, and in between of micro‐ and molecular scale of the macromolecular materials,
has become a hot spot along with the emerging needs for the design of multifunctional
environmentally‐, chemically‐ or biologically‐responsive nanocomposites for designing
microscale electronic, biological or catalytic devices. Among all the materials,
nanocomposites own the benefits of huge area‐volume ratio, nano‐scale phase separation
capability, and ideal modification of material properties due to the better mixing simply a
small enough size scale. Especially for nanofibers, due to the super high surface area and
porosity as high as 50~98%, nanofibers have become excellent candidates with the specific
nanostructure for applications in different areas including: biomaterial scaffolds as in vitro
extracellular matrix (ECM) in tissue engineering; carrier for controlled drug delivery; novel
textiles such as anti‐microbial sutures; wound healing dressing or chemical‐protective
military uniforms; ultrafiltration membranes; nanocomposites for material reinforcement;
and catalysts carrier etc. as will be elucidated in the “Application” section in detail.
The size scale of so‐called nanofibers is usually from sub‐micron down to several
nanometers. There are a lot of different types of methodology for the fabrication of
nanofibers, including molecular self‐assembly, anisotropic crystal growth, atomic deposition
and lithography, templating etc., and the most important, electrospinning. By applying the
electrostatic field to a polymer solution or melt jet, this seemingly simple process can create
different forms of nanofiber mats with different nanostructures, e.g. non‐woven nanofiber
mats, aligned nanofiber yarns, nanofibers with core‐sheath structure, nanofibers with
biofunctionally modified surfaces, nano or submicron tubes, nanofibers with porous
surfaces, nanofibers with attached nano‐particles etc. Along with its versatility lies the best
virtue of this method: via electrospinning people can get nanofibers composed of almost all
kinds of organic and inorganic nanocomposites besides the single‐component nanofibers. A
great number of materials, including natural biopolymers such as DNA, synthesized polymer
blends, nanocomposites of ceramics, even metal‐oxides or carbon nanotubes have already
been fabricated into nanofibers from electrospinning.
By controlling the material components or processing parameters, different structures
and morphologies of the nanofibers can be achieved according to the design requirements.
Electron microscopy techniques such as scanning electron microscopy (SEM), transmission
electron microscopy (TEM), atomic force microscopy (AFM), confocal microscopy (CM) etc.
can be applied to observe the nanofiber morphology and topology or intrinsic
nanostructures e.g. core‐sheath structure, and fluorescence microscopy is widely used in
biomaterial related characterization since it can avoid damage to the living cell from strong
electron beams; Spectroscopy techniques such as X‐ray photoelectron spectroscopy (XPS),
X‐ray diffraction spectroscopy (XRD), Raman spectroscopy etc. can be applied to
characterize the chemical information of the nanofibers. Recently development of chemical
imaging by those spectroscopy methods has made the analysis of nanofibers even easier
and visualized.
In this chapter, we aim to include the information about every aspect of nanofibers,
especially polymeric nanofibers, as widely as possible. The size scale of nanofibers that we
are discussing is at the order from 10nm to 1μm, as is for most of the polymeric nanofibers.
Information about certain types of pertinent inorganic ceramic nanofibers will be partly
included as well, whereas more comprehensive knowledge about inorganic ceramic
nanofibers especially carbon nanofibers and nanotubes can be found elsewhere in vast
amount of other publications. Introduction of the history, structure, processing or
characterization methodologies and applications of polymeric nanofibers in different
categories can be found in the following sections. Electrospinning will be emphasized as the
dominant technology among all nanofiber processing techniques due to its vast material
applicability and comparatively large fiber production scale. Other methods with
applications will as well be briefly introduced. Examples will be given along with directions
to more detailed and profound descriptions from related research groups and references.
2 PROCESSING
2.1 Overview of Nanofiber Processing
Conventionally, fibers or strands at millimeter or micron scale can be fabricated by
mechanical extrusion or spinning process. To obtain fibers at submicron down to
nanometer scale, innovative methods such as controlled one‐dimensional anisotropic
nucleation and crystallization growth (nanofibers with a diameter scale at the order of
1~100s nm), template synthesis (1~100s nm), molecular self‐assembly (1~10s nm), phase
separation (10s nm~1μm), and electrospinning (10nm~10μm) etc. have emerged in recent
decades 1‐3. Among all of these approaches, electrospinning has become the most powerful technique that can fabricate versatile types of nanofiber or nanofiber composites in both
organic and inorganic categories at a relatively large mass production scale. Hence it will be
illustrated as the major technique for the manufacture of nanofibers in the next section.
Several other approaches and concepts are introduced here briefly at this point merely to
provide an overview of nanofiber processing.
Anisotropic crystallization growth can be applied to create one‐dimensional inorganic
nanorods or wires at the size scale of 1~100nm or higher, if needed. However only materials
possessing a natural and highly anisotropic crystal structure can be employed in this
method, such as poly(sulphur nitride) (SN)x and many inorganic minerals like chrysolite that
exhibit a fibrous crystalline growth behavior. Chemical reactions such as sonochemical
approach are usually needed for the processing of these types of inorganic one‐dimensional
nanofiber growth. Xia and co‐workers created a series of inorganic nanowires with this
method and included their systematical research work in a vastly cited review paper 3. When the crystallization growth is based on a template, it becomes template synthesis.
Template synthesis is another commonly‐used approach mostly to produce inorganic
nanofibers e.g. carbon nanotubes and nanofibers 4 or conductive polyaniline (PANI) 5, 6, polypyrrole (PPy) 7 etc. Just as its name implies, a template is needed to generate the target nanostructure in situ with its morphology complementary to the original template, and in
some cases be removed after the target nanostructure is formed. This approach is often
combined with other process such as chemical vapor deposition 8 or electrodeposition 9 in order to grow the one‐dimensional nanostructure perpendicular to the template surface.
There are many other ways of template synthesis, most of which depend on the design of
the template. Xia and coworkers review of one‐dimensional nanostructures talked about
template synthesis extensively as well 3. Shankar and Raychaudhuri reviewd the fabrication of multicomponent oxides 10.
Molecular self‐assembly is mostly applied in biological regime, including
intramolecular and intermolecular self‐assembly. It utilizes the non‐covalent chemical
interactions of molecules, such as hydrophobicity or hydrophilicity, hydrogen bonding,
electrostatic charge effects, van der Waals forces, and other special interactions like π‐π
interaction etc., of a certain part of the molecules, to form assembly multi‐molecular
complex structures. The intramolecular self‐assembly process is often reversible and
derived spontaneously from unorganized molecular mixture to form well‐defined secondary
or tertiary structures, most of the cases occurring in biological systems. A good example of
the intramolecular self‐assembly would be the “protein folding” behavior. The
intermolecular self‐assembly can either be spontaneously, or induced by environmental
change such as solvent or temperature change under some circumstances, to form so‐called
“supramolecular assemblies”. The formation of micelles in solutions and quaternary
architectures formed by protein‐protein interactions can all be good examples of
intermolecular self‐assembly. The importance of supramolecular lies in creating biomimic
structures or designing coded structures for various application purposes in nanotechnology.
This method is comparatively new and becoming prosperous in recent decade. In 1987,
when Donald J. Cram, together with Jean‐Marie Lehn, Charles J. Pedersen was awarded
Nobel Prize in recognition of their contribution in the supramolecular chemistry. For the
purpose to produce biocompatible and biodegradable fibrous structures, molecular self‐
assembly has been extensively studied to produce scaffolds as extracellular environment for
tissue engineering. Amphiphilic peptide sequences 11‐14 and ionic self‐complementary peptides 15 are often employed for creating the self‐assembling nano fibrous or tube structures.
Phase separation is usually used to create porous foaming materials composed of
inorganic polymers. Whereas by controlling the gelation temperature, solvent, polymer
concentration etc. fibrous structure can be formed via this method as well. Smith and Ma
reported the thermally‐induced formation of poly(L‐lactic acid) (PLLA) fibrous matrix from
tetrahydrofuran (THF) solutions. They believed that the process occurred through spinodal
liquid‐liquid phase separation and consequential crystallization of the polymer‐rich phase by
taking five basic steps: “polymer dissolution, phase separation and gelation, solvent
extraction from the gel with water, freezing and freeze‐drying under vacuum” 16. The fiber diameter is at 50~500nm scale, and the porosity of the three dimensional structure can be
as high as 98%. Yang et al. from Ramakrishna’s group as well achieved similar results of PLLA
nanofibrous structure from phase separation with the diameter of 50~350nm 17.
2.2 Electrospinning Technology
2.2.1 History of Electrospinning
Although the research related to electrospinning technique was not blooming until
middle 1990s, the recognition of this process has been almost 100 years. The first person
who investigated the equilibrium of liquid charged with electricity, and provided the
concept of “Rayleigh instability” is Rayleigh at the end of 19th century 18. Zeleny tried to measure the electrical discharge from liquid points to a grounded metal plate, and
concluded that the charge on the liquid points is considerably smaller than on the metal
points 19, 20. In 1930s, a series of patents were issued to Formhals 21, 22. He tried to build up an ideal electrospinning setup that could continuously generate electrospun yarns, and at
the same time renovated the setup to produce composite fiber webs in his later patents 23. However, since the first electron microscope prototype was not created until 1933 by
German physicist Ernst Ruska (one of the two Nobel Prize winners in Physics because of his
contribution to EM in 1986) and Maximillion Knollin, due to the limitation of
characterization methods it was probably impossible for researchers to observe the
nanostructure image of electrospun fibers at that time.
Still, fundamental research about electrospinning was continued before practical
application demands emerged. Taylor studied the cone shape of polymer droplet with
different viscosity at the charged tip under electrostatic field, which was lately described as
a prerequisite for a stable electrospinning jet and named after him with “Taylor cone” by
following electrospinning researchers 24, 25. At the same time, Simons applied for a patent for his design of an apparatus to produce patterned non‐woven fabrics by “electrically‐spun
filaments” 26. With the evolution of characterization techniques of electron microscopy and spectroscopy, from the early 1970s researchers were able to analyze the structural
morphology of electrospun fibers. Baumgarten produced acrylic microfibers by
electrospinning of acrylic resin with different concentrations in DMF solution 27. He tried to
study the relationship between process parameters such as solution concentration, feeding
rate, and voltage with the fiber diameter, and as well took the “microflash” photographs of
the spinning jet at different conditions. Larrondo and Manley 28‐30 were the first to electrospin polyethylene and polypropylene melts. It was as well believed that the liquid
jets were atomized under electrostatic field. Hayati and Bailey investigated the effects of
electric field on “electrohydrodynamics spraying” of liquids, and concluded that only
semiconductive liquid with a conductivity range of 10‐6~10‐8 (Ωm)‐1 can form a stable jet with Taylor cone 31‐33.
With increased understanding of the potential applications in nanotechnology and
biotechnology, and the maturity of characterization methodology on almost every aspect of
nanostructure characterization such as morphology, chemical information and rheology
measurements, the research of electrospinning started to thrive from middle 1990s. The
first group that started comprehensive research on electrospinning was Reneker’s group from University of Akron. They produced poly(p‐phenylene terephthlamide) (PPTA) fibers at
~500nm diameter via an electrospinning setup with a grounded water bath as the collector,
and as well characterized both of the fiber morphology and crystallinity 34. They as well investigated the effects of processing parameters on the electrospinning of polyethylene
oxide (PEO) with different concentrations 35. In 1996 they published the first review on electrospinning process based on their electrospinning work with more than 20 different
electrospun polymeric nanofibers from polymer solutions or melts 36, and afterwards several papers regarding the general mechanism and process parameter effects on the
electrospun fiber morphology 37, 38. Rutledge’s group from Massachusetts Institute of Technology published a series of paper regarding their systematic research on
electrospinning mechanism from 2001 39‐42, and concentrated on the electrospinning of polymer blends 43 or nanocomposites 44 subsequently. Xia’s group from University of Washington successfully produced ceramic nanofibers 45, 46, and obtained nanotubes and core‐sheath structure by designing the fiber collector geometry 47, 48. Chu’s group from the
State University of New York at Stony Brook tried to produce bioabsorbable nanofiber
membrane 49, and scaffold carrier with controlled release of incooperated target molecules 50 for biomedical engineering using electrospinning process. Ramakrishna’s group from National University of Singapore concentrates on electrospinning of biocompatible
polymeric nanofibers suitable for biomedical and tissue engineering applications 51, 52 with different fiber alignment technique 53.
Other than these groups, there are a lot of other researchers working hard on
improving the process and bringing the electrospinning technique into application.
Especially after 2002, electrospinning has caught the attention of the researchers in world
wide and become a real hot area. The annual publications increased 5 times from year 2002
to 2006, as shown in Figure. 1. Among the publications, many high quality reviews which
covered both theoretical mechanism and application sides of electrospinning have been
published by generations, either generally, or on specific topics 48, 53‐56.
2.2.2 Fundamentals of Electrospinning
The typical scheme of basic electrospinning setup is shown in Figure. 3. It is composed
of at least a high‐voltage power supply (typically 1~30Kv), a reservoir for polymer solution
or melts which can provide stable flow rate (typically 1~ 50 μl/min) through a conductive
spinneret, and a grounded collector for the deposit of fiber mats. Usually a syringe pump
can be used to generate a steady flow rate of the polymer solution or melts continuously. If
ignoring other environmental effects, without the electric field, the slowly flowing liquid
droplets will form and drop at the tip of the spinneret by the balance of only two forces:
surface tension and gravity. When an electrostatic potential is applied between the
spinneret and the collector, a point‐to‐plate type of electrostatic field will form, which will
charge the surface of the droplets, thereby cause electrostatic repulsion force to form
besides the surface tension and gravity. Since the effect of gravity is very small compared to
the electrostatic force in electrospinning, it will be omitted in following discussions. With
the increase of electric field, the combined effect from electric force and surface tension
changed the shape of the droplet from a meniscus to a cone‐shaped structure known as
“Taylor cone” 25, until the gradient of electric field can finally break the droplet into a liquid jet.
As the jet is traveling, if it’s from a solution, the solvent will keep evaporating so that
the concentration of the solution keeps changing, which in turn causes the change in the
surface tension, viscosity, viscoelasticity and conductivity properties of the jet subsequently.
At the same time due to the Coulomb’s law, the electrostatic repulsive force charged on the
jet surface would try to increase the surface area of the jet by enormously decreasing the
jet diameter along with the jet thinning caused by the actual loss of solvent, which as well
happens in the polymer melts system. On the other hand the surface tension would
decrease the surface area of the jet by separating the continuous jet flow to droplets, and
hold back the speed of the jet to reach a very high order to where the electric force is
pushing. The combination of all these effects will break the equilibrium status for the jet to
stay stable and straight. Therefore after a certain length of stable stream, the jet will enter a
bending instability regime and start to twist by loops 38. If the solution is dilute with an enough inter‐ or intra‐ molecular entanglement less than needed, the jet will experience an
separating process along the axis into particles of the solutes deposited on the collector,
defined as “electrospraying”; if the solution can achieve a high enough inter‐ or intra‐ molecular entanglement but not too high to stop the jet motion, the jet will experience a
high‐speed whipping process, and smooth non‐woven fibers at micro to nano scale can be
collected from the collector, defined as “electrospinning”. In order to observe the whipping process, a high‐speed photograph must be taken instead of low‐speed one, which could be
the reason of misunderstanding the unstable region. As shown in Figure. 4, the so‐called
“splaying process” was believed actually the more apparent phenomena caused by the
whipping motion at high frequency 41, although some bifurcation and jet splitting does occur at certain spots 38. Recently more complicated jet structures in the instability regime
have as well been observed, e.g. garland structure 57 and branching structure 58 forming from the electrospinning of PCL solution, which is a similar but more complicated motion
based on the whipping process caused by the bending instability.
In general, a jet stably beginning with a Taylor cone is preferable for the
electrospinning of nanofibers with uniformly distributed geometric and mechanical
properties. To acquire a stable electrospinning process, an optimized combination of
appropriate material properties and process operational parameters needs to be taken into
account, which can be categorized into inertial, electrostatic, hydrostatic, rheological and
geometric factors.
2.2.3 Modeling of Electro‐driven Jet
The modeling of the electrospinning jet can be traced back to Rayleigh who the first
expressed the interest in the liquid jet present in an electrostatic field as mentioned in the
electrospinning history section. A more systematic and fundamental research was done by
Taylor, who showed that the prerequisite for a stable liquid jet to form under the
electrostatic field is to acquire an angle of 49.3o of the Taylor cone 24. He as well established a relationship of the critical potential Vk with regard to the distance between the electrodes
H, length of the spinneret L, inner radius of the spinneret R, and surface tension of the fluid
γ 25:
(
2cos49.3)
(0.09) 2 3 2 ln 4 2 22 ⋅ ⋅
⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −
= πRγ
R L L
H
Vk o (1)
Hendricks et al. suggested the definition of the minimal spraying potential of a
conducting drop suspended in the air with regard to the jet radius r and surface tension γ 59:
(
20)
12 300⋅ ⋅π
⋅ ⋅λ
= r
Vc (2)
The first systematic mathematical modeling of the electrospinning jet in the bending
instability area was proposed by Reneker et al. and applied to simulate the electrospinning
jet of viscoelastic polymeric system 38. The model shows that the longitudinal stress caused by the electric field stabilizes the straight jet for some distance, until a lateral perturbation
caused by the electrostatic repulsive force charged on the jet surface grows high enough to
drive the jet into a bending instability area. The parameters taken into account in their
model include voltage, distance between the electrodes, surface tension, and elastic
modulous etc. Three dimensional paths of continuous jets were calculated from the straight
jet region to the bending instable region, and compared to the experimental data obtained
by high speed videographic observations. In their subsequent work 60, as shown in Figure. 5, they calculated the bending electric force to establish an analogy between the electrically
driven and the aerodynamically driven bending instability. The solvent evaporation and
polymer solidification that showed a strong effect on the modeling results were as well
taken into account by incorporating a series of dimensionless correlation numbers
representing the solution hydrodynamic and material properties. Furthermore, they set up
self‐similar hyperboidal approximation to predict the stationary critical shapes of inviscid,
Newtonian, viscoelastic and purely elastic fluid droplets 61, and approached the shape of Taylor cone with a half angle of 33.5o instead of 49.3o.
Hofman et al. from Rutledge’s group differentiated the instability concept into the
combination of: the classical (axisymmetric) Rayleigh instability, electric field induced
axisymmetric and whipping instabilities to investigate the stability of a charged fluid jet in a
tangential electrostatic field 39. By employing Newton’s law, conservation law and Coulomb’s integral equation for the electric field, they derived a set of axisymmetric
equations to model the jet electrohydrodynamics under instable perturbation. The fluid
system needs to be dilute under low shear and in the absence of high degrees of extension
in order to satisfy Newtonian fluid requirements. Conductivity, viscosity, surface tension,
dielectric constant, potential, distance between the electrodes, and surface charge density